Mathematics

Inverse problems for nonlinear stationary equations

A. Sh. Lyubanova

Siberian Federal University, Svobodnyi ave., 79, Krasnoyarsk 660041

Abstract: Identification of the unknown constant coefficient in the main term of the partial differential equation $-kM\psi_1(u)+g(x)\psi_2(u)=f(x)$ with the Dirichlet boundary condition is investigated. Here $\psi_i(u),\quad i=1,2,$ is a nonlinear increasing function of $u$ and $M$ is a second-order linear elliptic operator. The coefficient $k$ is recovered on the base of additional integral boundary data. The existence and uniqueness of the solution to the inverse problem with a function u and a positive real number k is proved.

Keywords: inverse problem, boundary value problem, second-order elliptic equation, existence and uniqueness theorem, filtration.

UDC: 517.95

Received: 03.03.2016

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